Federal Grant Award Summary

The National Science Foundation's Division of Mathematical Sciences awarded $400,000 to Harvard University under the Mathematical and Physical Sciences program (CFDA 47.049) for a three-year project (June 1, 2026 – May 31, 2029) focused on developing tensor decomposition algorithms for multi-context data analysis. The primary deliverable is a suite of new computational algorithms designed to analyze complex systems that vary across different contexts—such as biological processes across diseases or word meanings across literary genres. These algorithms will address a longstanding theoretical challenge in tensor decomposition by employing basis transformation methods and building decompositions incrementally, improving scalability, reliability, and interpretability compared to existing approaches.

The research will produce both theoretical and practical outputs: rigorous mathematical proofs establishing the performance guarantees of the proposed algorithms using numerical analysis and real algebraic geometry, along with validated computational implementations. These tensor decomposition methods will be applied to real-world problems including analyzing gene program variability across diseases and examining word usage patterns across literary genres, thereby enhancing artificial intelligence models for biological and linguistic data analysis. The project emphasizes single-term decomposition construction to ensure compatibility across different rank levels, enabling simultaneous multi-context comparison without requiring pairwise context comparisons.